Module Catalogue 2024/25

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

This module aims to cover the Pure Maths content of the A2 level Maths curriculum to prepare students for the rigor of stage 1 modules in Mathematics, Physics and Engineering.

Students will further develop skills in algebraic manipulation, be introduced to a wider range of functions and to further explore elementary calculus and vectors. Students will develop skills and understanding commensurate with their eventual peers on their destination programme.

Outline Of Syllabus

1.Algebraic methods (Algebraic fractions, partial fractions, algebraic division)
2.Functions and graphs (modulus function, composite functions, inverse functions, combining transformations)
3.Sequences and Series (Arithmetic/Geometric, Sum and sum to infinity, sigma notation, recurrence relations)
4.Binomial Expansion ((1+x)^n, (a+bx)^n, using partial fractions)
5.Radians (radian measure, arc length, area of sector/segment, solving trig equations, small angle approximation)
6.Trigonometric Functions (Sec, Cosec, Cot, Inverse trigonometric functions)
7.Trigonometry and modelling (Addition formulae, double angle formulae, Solving trig equations, simplifying acosx +/- bsinx, proving trig identities)
8.Parametric equations (Introduction, using trig identities, curve sketching, points of intersection)
9.Differentiation (Differentiating sin, cos, exp, log, product/quotient and chain rules, parametric and implicit differentiation, second derivatives, rates of change)
10.Numerical Methods (locating roots, iteration, Newton-Raphson)
11.Integration (Integrate f(ax+b), standard functions, reverse Chain rule, by substitution, by parts, using partial fractions, finding areas, solving differential equations, trapezium rule)
12.Vectors (3D cords, 3D vectors, solving geometric problems)

Intended Knowledge Outcomes

At the end of this module students should have mastered a suite of algebraic techniques to enable them to integrate and differentiate a plethora of functions. They will know the key rules to differentiate and integrate general functions. They will also know numerical methods used to locate roots and find derivatives. Students will know about sequences and series and how to find limits. Students will also understand vectors in 3-dimensions. Students will also have a knowledge of more advanced trigonometric functions and identities.

Intended Skill Outcomes

At the end of this module students will be able to differentiate and integrate general functions using calculus rules. They will be able to analyse 3d vector problems using geometrical methods and find the limits of some standard series.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Asynchronous lectures are used for the delivery of theory and explanation of methods, lectures broaden this understanding and provide illustrative examples, and can be used for giving general feedback on marked work.

Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity is vital to ensure students have the best chance of success in their destination programme.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

General Notes

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